不连续治疗策略下一类非线性SIR模型的全局稳定性

Global stability of SIR model with nonlinear incidence and discontinuous treatment

研究一类具有不连续治疗策略和非线性发生项的SIR模型。首先运用右端不连续的微分方程理论定义模型的Filippov解,然后证明该模型的全局行为由阈值R0确定,即当R0≤1时,无病平衡点全局渐近稳定。

A class of SIR model with discontinuous treatment and nonlinear incidence is proposed. Firstly, we define the Filippov solution of the system by using the theory of the differential equations with discontinuous right-hand side. We prove that the global dynamics of each discontinuous SIR model is fully determined by a single threshold parameter R0, which indicates that the unique disease-free equilibrium is globally asymptotical stable if R0≤ 1.